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Expressions for the perfect matching numbers of cubicl x m x n lattices and their asymptotic values

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Abstract

A general expression of the perfect matching number for thel x m x n cubic lattice was conjectured and examined for infinitely large systems. The asymptotic value of the square of the perfect matching number was calculated by numerical integration. The present treatment will give a key to obtain the true analytic solution of the perfect matching numbers for the 3-dimensional lattices.

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Authors and Affiliations

  1. Division of Material Science, Graduate School of Environmental Earth Science, Hokkaido University, 060, Sapporo, Japan

    Hideyuki Narumi & Hideaki Kita

  2. Department ofInformation Sciences, Ochanomizu University, 112, Bunkyo-ku, Tokyo, Japan

    Haruo Hosoya

Authors
  1. Hideyuki Narumi
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  2. Hideaki Kita
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  3. Haruo Hosoya
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Narumi, H., Kita, H. & Hosoya, H. Expressions for the perfect matching numbers of cubicl x m x n lattices and their asymptotic values. J Math Chem 20, 67–77 (1996). https://doi.org/10.1007/BF01165156

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  • DOI: https://doi.org/10.1007/BF01165156

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